Implicit differentiation/ partial differentiation

**CookieC** · July 26th 2010, 04:35 PM

How do i find the partial derivative in terms of Y from the equation z = x^y even if X is held as a constant i dont know how to differentiate it :S

**CookieC** · July 26th 2010, 04:36 PM

Actually, is the answer just zero?

**bondesan** · July 26th 2010, 05:24 PM

Follow these steps, where $z_y$ means the derivative of z with respect of y.

$\displaystyle{z=x^y}$

$\displaystyle{ln(z) = y\cdot ln(x)}$

$\displaystyle{\frac{\partial}{\partial y} ln (z) = \frac{\partial}{\partial y}\left(y\cdot ln (x)\right)}$

$\displaystyle{\frac{z_y}{z} = ln (x)}$

$\displaystyle{z_y = z\cdot ln (x) = x^y\cdot ln (x)}$

Got it?

Thread: Implicit differentiation/ partial differentiation

LinkBack

Thread Tools

Display

Implicit differentiation/ partial differentiation

Similar Math Help Forum Discussions

implicit Partial differentiation

[SOLVED] Implicit partial differentiation. Need my answer checked please

Implicit Differentiation of Partial Derivatives

Differentiation and Implicit Differentiation

Calculating partial derivatives by implicit differentiation of the Law of Cosines

Search Tags